The Beovox S80 woofer is very friendly when it comes to refoam'ing so you may end up with a good result but I can assure you that the method you describe won't be adequate for many other types of woofers, Redline 140 springs to mind, where tolerances are extremely tight.
Always, and I do mean always re-shim the coil and fixate it while the foam sets. If you don't chances are that the coil will start rubbing against the magnet and eventually destroy the speaker beyond repair. Incorrect mounting, skew, offset or uneven load on the spider, even of the tiniest amount won't correct itself, it will only get worse as the stressed part(s) wear and give.
It's a great speaker and definitely worth restoring.
Oh, and do check the solders at the PCB where the spade connectors are mounted, they tend to break. Use solder with a hint of silver in it, it will be the best thing to use in this vibrating environment.
Martin